Some Generalized $q$-Bessel Type Wavelets and Associated Transforms

Abstract

In this paper wavelet functions are introduced in the context of $q$-theory. We precisely extend the case of Bessel and $q$-Bessel wavelets to the generalized $q$-Bessel wavelets. Starting from the $(q,v)$-extension $(v = (α,β))$ of the $q$-case, associated generalized $q$-wavelets and generalized $q$-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.